Comment on Vertical Asymptotes

richardt

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This post was moved from: http://www.freemathhelp.com/forum/threads/85892



BTW, with regard to Quaid's response, vertical asymptotes do not necessarily occur whenever a denominator has value zero. This condition alone only implies the function to be undefined.

The line x = r is a vertical asymptote of function, f, if the limit of f as x approaches r does not exist (i.e., f tends toward +/- infinity as x approaches r).

Consider f(x) = (x2 - 1) / (x - 1). This function is undefined for x = 1, but the limit as x approaches 1 is 2. To see this, notice that factoring x2 - 1 gives,

f(x) = (x+1)(x-1)/(x-1) = x + 1 ; x not = 1. Hence the graph of f is just a line with a missing point at (1, 2). no asymptote.

Rich
 
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Thank you for your comments.

I'm trying to keep it "simple", in that thread, as the OP seems very inexperienced.

I have no idea whether this person has been exposed to limits.

Cheers :cool:
 
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